2 /* @(#)e_atanh.c 1.3 95/01/18 */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
16 static char rcsid[] = "$FreeBSD$";
21 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
24 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
28 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
31 * atanh(x) is NaN if |x| > 1 with signal;
32 * atanh(NaN) is that NaN with no signal;
33 * atanh(+-1) is +-INF with signal.
38 #include "math_private.h"
40 static const double one = 1.0, huge = 1e300;
41 static const double zero = 0.0;
44 __ieee754_atanh(double x)
49 EXTRACT_WORDS(hx,lx,x);
51 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
55 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
57 if(ix<0x3fe00000) { /* x < 0.5 */
59 t = 0.5*log1p(t+t*x/(one-x));
61 t = 0.5*log1p((x+x)/(one-x));
62 if(hx>=0) return t; else return -t;